My toenail has grown back strange. A mound of skin-like material is growing out of the nail bed. So the toe nail grows up and over the mound.

Toe bone injury. It sounds as though that "mound of skin" may be the result of injuring the toe bone just under the nail bed. Occasionally, the bone, when injured responds by a sudden growth spurt. As it grows upward, it raises the nail bed up and can cause a nail distortion as you have described. An r-ray will usually confirm the event. The treatment involves removing the boney spur. Known as subungual exostosis.